Timescales in creep and yielding of attractive gels

The stress-induced yielding scenario of colloidal gels is investigated under rough boundary conditions by means of rheometry coupled with local velocity measurements. Under an applied shear stress sigma, the fluidization of gels made of attractive carbon black particles dispersed in a mineral oil is shown to involve a previously unreported shear rate response (gamma) over dot(t) characterized by two well-defined and separated timescales tau(c) and tau(f). First (gamma) over dot decreases as a weak power law strongly reminiscent of the primary creep observed in numerous crystalline and amorphous solids, coined the Andrade creep. We show that the bulk deformation remains homogeneous at the micron scale, which demonstrates that whether plastic events take place or whether any shear transformation zone exists, such phenomena occur at a smaller scale. As a key result of this paper, the duration tau(c) of this creep regime decreases as a power law of the viscous stress, defined as the difference between the applied stress and the yield stress sigma(c), i. e. tau(c) similar to (sigma - sigma(c))(-beta), with beta = 2-3 depending on the gel concentration. The end of this first regime is marked by a jump of the shear rate by several orders of magnitude, while the gel slowly slides as a solid block experiencing strong wall slip at both walls, despite rough boundary conditions. Finally, a second sudden increase of the shear rate is concomitant with the full fluidization of the material which ends up being homogeneously sheared. The corresponding fluidization time tau(f) robustly follows an exponential decay with the applied shear stress, i.e. tau(f) - tau(0) exp(-sigma/sigma(0)), as already reported for smooth boundary conditions. Varying the gel concentration C in a systematic fashion shows that the parameter sigma(0) and the yield stress sigma(c) exhibit similar power-law dependences with C. Finally, we highlight a few features that are common to attractive colloidal gels and to solid materials by discussing our results in the framework of theoretical approaches of solid rupture (kinetic, fiber bundle, and transient network models).